Return-Path: Received: (majordomo@vger.kernel.org) by vger.kernel.org via listexpand id S265253AbUAESJr (ORCPT ); Mon, 5 Jan 2004 13:09:47 -0500 Received: (majordomo@vger.kernel.org) by vger.kernel.org id S265254AbUAESJr (ORCPT ); Mon, 5 Jan 2004 13:09:47 -0500 Received: from 81-5-136-19.dsl.eclipse.net.uk ([81.5.136.19]:38858 "EHLO vlad.carfax.org.uk") by vger.kernel.org with ESMTP id S265253AbUAESJo (ORCPT ); Mon, 5 Jan 2004 13:09:44 -0500 Date: Mon, 5 Jan 2004 18:09:27 +0000 From: Hugo Mills To: Davide Libenzi Cc: Linus Torvalds , Andries Brouwer , Daniel Jacobowitz , Rob Love , rob@landley.net, Pascal Schmidt , Linux Kernel Mailing List , Greg KH Subject: Re: udev and devfs - The final word Message-ID: <20040105180927.GB17606@carfax.org.uk> Mail-Followup-To: Hugo Mills , Davide Libenzi , Linus Torvalds , Andries Brouwer , Daniel Jacobowitz , Rob Love , rob@landley.net, Pascal Schmidt , Linux Kernel Mailing List , Greg KH References: <20040105172900.GA359@ucw.cz> Mime-Version: 1.0 Content-Type: multipart/signed; micalg=pgp-sha1; protocol="application/pgp-signature"; boundary="GID0FwUMdk1T2AWN" Content-Disposition: inline In-Reply-To: X-GPG-Fingerprint: B997 A9F1 782D D1FD 9F87 5542 B2C2 7BC2 1C33 5860 X-GPG-Key: 1C335860 X-Parrot: It is no more. It has joined the choir invisible. X-IRC-Nicks: hugo darksatanic User-Agent: Mutt/1.5.4i Sender: linux-kernel-owner@vger.kernel.org X-Mailing-List: linux-kernel@vger.kernel.org Content-Length: 2442 Lines: 72 --GID0FwUMdk1T2AWN Content-Type: text/plain; charset=us-ascii Content-Disposition: inline On Mon, Jan 05, 2004 at 09:52:45AM -0800, Davide Libenzi wrote: > On Mon, 5 Jan 2004, Vojtech Pavlik wrote: > > > On Mon, Jan 05, 2004 at 08:13:26AM -0800, Linus Torvalds wrote: > > > > > But the thing is, some things you simply _cannot_ number. For example, a > > > two-dimensional space is innumerable - you need more than one integer > > > number to look things up. So is the set of real numbers (but not the set > > > of fractions), etc etc. > > > > Two dimensional discrete space (*) is enumerable. Just start at [0,0] > > and assign numbers going around the center in a growing spiral (**). > > That way you assign a number to every point in that space. This is very > > similar to the trick used to demonstrate fractions are enumerable. > > Vojtech, a spiral (in the math sense) won't work because whatever > continuos function you choose for the radius, you are going to skip > integers when the radius grows (and duplicate them when it's small). Also, > IIRC, fractions are enumerable because they're a mapping from two > enumerable spaces (integers): F = F(I1, I2) = I1 / I2. I think he meant something like this: ( 0, 0) ( 1, 0) ( 0, 1) (-1, 0) ( 0, -1) ( 2, 0) ( 1, 1) ( 0, 2) (-1, 1) (-2, 0) (-1, -1) etc. Rationals are countable since they're the product of the integers (numerator) and the natural numbers without zero (denominator). You can count them in a similar way to the above "spiral", making sure that you don't count 1/2 and 2/4 as two different numbers. :) Hugo. -- === Hugo Mills: hugo@... carfax.org.uk | darksatanic.net | lug.org.uk === PGP key: 1C335860 from wwwkeys.eu.pgp.net or http://www.carfax.org.uk --- Try everything once, except incest and folk-dancing. --- --GID0FwUMdk1T2AWN Content-Type: application/pgp-signature; name="signature.asc" Content-Description: Digital signature Content-Disposition: inline -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.2.4 (GNU/Linux) iD8DBQE/+ahXssJ7whwzWGARAoirAKCHaDflKMZIbmkdc0AMhkY9lB1BXwCePprk AsckPNphj0IJSRs3lSC4FKQ= =PgHX -----END PGP SIGNATURE----- --GID0FwUMdk1T2AWN-- - To unsubscribe from this list: send the line "unsubscribe linux-kernel" in the body of a message to majordomo@vger.kernel.org More majordomo info at http://vger.kernel.org/majordomo-info.html Please read the FAQ at http://www.tux.org/lkml/